Area Between Curves: Ace AP Calculus Like a Pro

Finding the Area Between Curves Expressed as Functions of y

Abigail Young

6 min read

Next Topic - Finding the Area Between Curves That Intersect at More Than Two Points

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Study Guide Overview

This study guide covers finding the area between curves expressed as functions of y. It explains how to set up the integral using horizontal slices and integrate with respect to y. It includes the formula for area calculation and provides practice problems, including one using a calculator. The guide reviews finding intersection points and emphasizes the difference between integrating with respect to x and y.

#8.5 Finding the Area Between Curves Expressed as Functions of y

Welcome back to AP Calculus with Fiveable! Today, we're delving into the fascinating world of finding the area between two curves expressed as functions of y. We've already tackled definite integrals and finding the area between two curves, so lets keep up the momentum! 🚀

#📏 Area Between Curves defined using $y$

The AP Calculus Exam often throws questions at you that involve finding the area between curves. Most of the time, it will be using functions defined using $x$ . To review that process, check out the following Fiveable Guide: Finding the Area Between Curves Expressed as Functions of x. The following image shows the difference between taking the area between curves with vertical slices, as we did in the last key topic, and horizontal slices, as we’ll do today!

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Finding area with horizontal slices vs finding area with vertical slices

Image Courtesy of Coordinated Calculus

In this case, we're dealing with functions expressed in terms of y. The key idea here is to use horizontal slices to break down the region between the curves into small rectangles. By summing up the areas of these rectangles, we can find the total area. It will be a very similar ...